[Smt-talk] Subdominant versus Predominant

[Ninov, Dimitar N]

Dear Thomas,

Thank you. Your concepts about modes are close to the manner some of us explain the subdominant function: IV is S, and II is SII (a subdominant on the second scale degree). 
I also agree with the existence of altered subdominant functions which contain the raised fourth scale degree - but only when they resolve into the tonic. Notice the difference: if D7 (or inverted D7) resolves to I, I6 and I6/4, I would categorize it as an altered SII, but if it resolves directly into V, I will mark it as V7/V. Because for me the function depends not only on the structure, but also on the resolution. When D7 resolves into I, I6, and I6/4 it does not toniccize a secondary tonic but reaffirms the main one (in the case of the cadential 6/4, D7 resolves into t a tonic structure if not a function). On the other hand, when D7 resolves into V, it treats it like a local tonic.

Your theory of modes sounds very interesting to me. I would love to learn more. As for the substitution of VI for I, this topic may easily fill pages of discussion. I personally agree that the mediants (III and VI) substitute for T when they appear after a dominant function, or when III appears between I and IV. However, I support the notion that this substitution is non-functional; it occurs on the basis of the relative stability that the mediants display in comparison with the other, more unstable S and D chords. This is due to the fact that they each share two common tones with the tonic. But a true functional substitution for me is impossible, for the center of gravity is only one in a key, and - most importantly - the mediants have a polar modality to the tonic; when the tonic is major, they are minor, and vice versa. Therefore, I am not convinced that a minor triad can be a functional substitute of a major tonal center, and that a major mediant can substitute for a minor tonal center.

When I studied harmony, some professors wanted us to mark the progression V-VI as D-Tvi (tonic on the sixth scale degree). Then I read the great theoretical treatise by Stepan Grigoriev "Theory of Harmony" and decided simply to mark the progression as D-VI, because of the reasons given above. 

Having said all of the above, I still remain very sympathetic to the notion of the tonic being substituted by VI or III - after all, functional or not, this substitution has been a main device of bringing variety and color to harmonic progressions. I teach some of the possible applications of the mediant chords along the line of T substitute. The other line is an S substitute for the Vi chord (VI-V) and a D substitute for the III chord (III-I). 

Thank you for those interesting points!

Dimitar

Dr. Dimitar Ninov, Lecturer
School of Music
Texas State University
601 University Drive
San Marcos, Texas 78666
________________________________________
From: Thomas Noll [noll at cs.tu-berlin.de]
Sent: Friday, February 24, 2012 3:29 PM
To: Ninov, Dimitar N
Cc: smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Subdominant versus Predominant

Dear Dimitar, dear Colleagues

I was also puzzled that Kostka and Payne consider IV a substitute for II. This is strange, given the fact that in classical and romantic music the typical subdominant bass is the 4th scale degree. II6 is a substitute for IV, not the other way around. In jazz, however, the II gets the upper hand, as II-V-I is the skeleton. Perhaps this is what confused the authors.

your question goes at the heart of a joint investigation by Karst De Jong and myself. We approach this issue from a different angle, which considers the fundament progression as a quasi-modal phenomenon. I say "quasi" because these functional modes have only thee essential notes rather than seven. They form modes of the so called "tetractys scale" or structural scale (Carey/Clampitt).
The roots of  IV V I and  II V I exemplify the first and second mode, respectively. We label them S D T in either case.  So far the basic idea.
But despite of the characterization of IV and II as the genuine subdominant scale degrees in the first and second functional modes, respectively, we also offer a concept of "functional chromaticism". The alteration interval in the world of functional modes, i.e. quasi the "augmented prime" in the internal language of the tetractys, is nothing but the usual minor third (in diatonic language).
In other words, within a first functional mode with the root of IV as the genuine subdominant scale degree there can still occur a fundament of II (or of V/V) which is then characterized as an "altered" IV rather than a genuine subdominant of a second functional mode. The analogous chromatic note in the second mode is the minor third below the tonic. That's typical for the turn around I VI II V I, where we regard the root of VI (or of V/II) as a functional alteration of the tonic degree.
For details see:
De Jong, Karst and Thomas Noll (2011): "Fundamental Passacaglia: Harmonic Functions and the Modes of the Musical Tetractys"<http://user.cs.tu-berlin.de/%7Enoll/FundamentalPassacaglia.pdf>, Agon, Carlos et. al. Mathematics and Computation in Music 2011, Berlin, Heidelberg: Springer: pp. 98 -114.
http://user.cs.tu-berlin.de/~noll/FundamentalPassacaglia.pdf
Sincerely
Thomas Noll



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Thomas Noll
http://user.cs.tu-berlin.de/~noll
noll at cs.tu-berlin.de<mailto:noll at cs.tu-berlin.de>
Escola Superior de Musica de Catalunya, Barcelona
Departament de Teoria i Composició

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